re:raw scores and appeals

Tree · Post by **Tree** » Thu Dec 24, 2009 3:07 pm

aaaaaaaagggghhhhhhhh ! cant get it to line up and have officially given up

Tree · Post by **Tree** » Thu Jan 07, 2010 5:15 pm

Hi all

As i can't get the table to print i will give the formulae so if anyone wants to convert a standardised score to a raw score you can do it by hand.For a standardised score (ss) and birth month (bm) (aug=1 jul=2 june=3 .... sept =12) the raw score rs is given by:

rs={({[(ss-100)/15]x12}+48.5)+[bm/2.5]}

ie. you subtract the standardised score by 100 and then divide by 15 to get the score as a number of standard deviations ie for a standardised score of 115 this is 115-100 = 15 , then 15/15 = 1 or for 120 this would be 120-100 = 20 then 20/15 = 1.33. (so in other words if you get 115 your score is one standard deviation above then mean score and if you get 120 your score is 1.33 standardard deviations above the mean score) To convert the number of standard deviation to a raw score difference from the mean you multiply the number of standard deviations by the modelled standard deviation for the test which for 2009 bucks tests was 12 (from the data i modeled). So for standardised score of 115 this is 1x12 = 12. You then add this to the mean for the test which i modeled as 48.5 for the 2009 test. So the raw score for 115 is 48.5 + 12 = 60.5 . You then need to make an age correction which i modeled as the month as a number (aug=1 to september =12) divided by 2.5 so for a september child it would be 12/2.5=4.8 and for an august child it would be 1/2.5 = 0.4 so for a standardised score of 115 an august child raw score would be 60.5 + 0.5 = 61 and a september child would be 60.5 + 4.8 = 65.3. This calculation fits pretty well for both tests and there only seemed to be a 1 mark difference between the first and second test.

There are some limitations of this analysis. It was only based on 15 data points from people who had requested their raw scores. It doesn't work v well for v high or low scores as it assumes a normal distribution (or more acuratly that the standard deviation is consistent across scores and ages) which it can't be because for example you can't get more than 80 in the test and so i would be doubtful of the significance with really high or low scores. Also the age correction is pretty crude and assumes that the mean raw score increases constantly with each month older by the same amount (0.4) i have no way of telling unless i get alot more data if this is true.

I hope this makes sense let me know if not. Also if you have some raw scores and they don't fit this calculation please let me know and i can alter the model.

ian35mm · Post by **ian35mm** » Thu Jan 07, 2010 6:24 pm

OK. I maybe a bit dense today - been ill for a while, but the bm weighting seems to greatest 'advantage' to those children who are the oldest in the year, the September kids. 12 marks for September and 1 for October?

What have I missed?

flossie · Post by **flossie** » Thu Jan 07, 2010 7:19 pm

Hi Tree,

Thanks for your answers to my questions and sorry for the delay in thanking you for this, somehow I missed your reply.

If only dd had been born two days later!!!

Tree · Post by **Tree** » Fri Jan 08, 2010 1:49 am

Hi ian35mm you are right that for children who are the oldest you effectively add to their raw score 12/2.5 or 4.8 for the same standardised score. This means that for the same standardised score of 115 the oldest child has to get 5 or so marks more in the test than the youngest ie its harder for them. If you rearrange the equation for to get the standardised score from the raw score then you subtract the marks off:

ss=(((((rs-(bm/2.5))-48.5)/12)x15)+100)

No problem flossie i suppose someone has to just miss passing wishing you all the best of luck

tree

Morning Glory · Post by **Morning Glory** » Fri Jan 08, 2010 9:14 am

Tree

Thank you for your equation very useful but I am confused too.

Surely September born children are the oldest in the school year and therefore for bm it should be Sept=1 Oct=2 Nov=3 Dec=4 ...... Aug=12 or am I missing something?

MG

Tree · Post by **Tree** » Fri Jan 08, 2010 11:40 am

hi morning glory you actually add more to their raw score the older they are when you are converting from a standardised score to a raw score. ( in know it sounds counter intuitive) this is because older children need to have higher raw scores for the same standardised score so for an AUGUST born child they only need 61 for a standardised score of 115 but a year older september born child would need a higher raw score of 65 to get a standardised score of 115

Morning Glory · Post by **Morning Glory** » Fri Jan 08, 2010 12:58 pm

Tree

Thanks - yes I can see that the older child need to get higher raw scores. Therefore should the BM not be (sorry got it round the wrong way in the last post).

bm - Sept = 12 Oct =11 Nov = 10 Dec = 9 Jan = 8 .................Aug = 1

Your original post with the original equation has

Oct=1 Nov=2 Dec=3 ..................Sept=12 - which is what is confusing me.

Or has all this white stuff just frazzled my brain cells completely or it might be I'm just so cold I can't function properly.

MG

Tree · Post by **Tree** » Fri Jan 08, 2010 2:10 pm

hi sorry guys wrote oct but meant aug doh!! yep for october in original post read august (HAVE EDITED IT NOW) so:

August 1
july 2
june 3
may 4
april 5
march 6
feb 7
jan 8
dec 9
nov 10
oct 11
sept 12

Morning Glory · Post by **Morning Glory** » Fri Jan 08, 2010 2:17 pm

Tree

Now that makes sense.

You have done a fantastic job working all this out, I still wouldn't know where to start.

Thanks

MG